In my opinion there's no better practice than playing Typing of the Dead. If losing in a game irks you even a little you'll definitely improve your typing speed by playing if your current speed is slow.
I've been toying with the idea of making a spiritual successor to this for years, always been too busy with work though. It's one of my favourite games of all time!
Maybe there's some artists/developers here that would want to collaborate to reduce the time burden a bit? :P
I used to make my babysitter play while I watched, because I was astounded she could do so well on hard. Now I play on X-Treme and see if I can make it to the end.
I remember when I was a kid X-Treme seemed impossible, I thought the developer put the difficulty in as a joke.
Nowadays I load the game up once every few months and I tend to beat X-Treme first shot every time, unless I get unlucky with the toxic sharks. It seems you need around 110-120wpm and decent reaction times to finish it.
And make sure I don't hit the wrong letter to start a new fish! That always manages to trip me up. That makes sense, my range is usually around 110. Damn I hate those toxic sharks!
Epistory: Typing Chronicles is another fairly recently released great indie typing game that even runs on Linux and supports layouts other than QWERTY such as COLEMAK and DVORAK.
What blew my mind with the site in the post, and what Typing of the Dead lacks, is that it shows you which fingers to use to type. I never before realized that in all my 15 years of typing, I only use my index and middle fingers. I'm going to use this site to train myself to type using all my fingers instead, which I'm fairly confident will lead to a speed and accuracy boost.
There was in fact an OS X version of TotD, called "Typing Of The Dead: Typing Lariat", and it was an universal binary too; I think I still had it on my mac a few months ago.
I don't think it's sold anywhere anymore; you should be able to find it on some abandonware website, with a bit of googling.
The menus are in japanese but the text to type is all either in english or at least uses english characters. If you want the proper english version you could try with wine, the tests on winehq seem to report decent compatibility.
https://www.youtube.com/watch?v=jslf5hJMtvs